If using rotisserie chicken, remove skin and bones, then shred or dice into bite-sized pieces. If using canned chicken, drain well and pat dry with paper towels.
In a large bowl, whisk together mayonnaise, Dijon mustard, hot sauce, and a pinch of salt and pepper.
Add the chicken, celery, red onion, and pickles to the bowl. Stir until everything is evenly coated.
Fold in the fresh dill or parsley. Taste and adjust seasoning—add more hot sauce, salt, or pepper as needed.
Cover and refrigerate for at least 30 minutes to let flavors meld. Serve cold.